Simulation of the Interaction of Waves with Granulated Layers in Shock Tubes

The basic equations and results of numerical modeling of the processes of interaction of an air shock wave with a sand barrier located at some distance from the closing end of the shock tube are presented. The processes are considered in a one-dimensional approximation, the dynamics of a sandy granular layer is modeled by the equations of a continuous elastic-plastic porous medium. The equations of gas dynamics and the dynamics of a granular medium are solved numerically on the basis of a single modified Godunov scheme. The processes of formation of shock waves affecting the barrier, the processes of formation of shock waves reflected from the ends of the shock tube and refracted shock waves are described. The protective effect of the sand screen is to reduce the pressure behind the front of the shock wave when it is reflected from the ends of the shock tube. In the absence of a gap between the end of the shock tube and its rear wall, no weakening effect was observed. The results of numerical simulation of gas-dynamic processes and processes of compression of sand layers, in general, correspond to experimental data.